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JCECE Engineering JCECE Engineering Solved Paper-2007

  • question_answer
    If \[x,\,\,\,y\] are any two elements of a Boolean lattice, then \[(x+y)\cdot (x+y')\cdot (x'+y)\] is equal to

    A) \[x+y\]                

    B) \[x\cdot y\]

    C) \[x'+y\]               

    D) \[x\cdot y'\]

    Correct Answer: B

    Solution :

    \[(x+y)\cdot (x+y')\cdot (x'+y)\]                 \[=\{(x+y)\cdot (x+y')\}\cdot (x'+y)\] (By using associative law of multiplication)                 \[=\{x+(y.y')\}\cdot (x'+y)\]                 \[=(x+0)\cdot (x'+y)=x\cdot (x'+y)\]                 \[=(x\cdot x')+(x\cdot y)\]                 \[=0+(x\cdot y)=x\cdot y\]


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